Handbook of Mass Measurement
Features
Summary
"How much does it weigh?" seems a simple question. To scientists and engineers, however, the answer is far from simple, and determining the answer demands consideration of an almost overwhelming number of factors.
With an intriguing blend of history, fundamentals, and technical details, the Handbook of Mass Measurement sets forth the details of achieving the highest precision in mass measurements. It covers the whole field, from the development, calibration, and maintenance of mass standards to detailed accounts of weighing designs, balances, and uncertainty. It addresses the entire measurement process and provides in-depth examinations of the various factors that introduce error.
Much of the material is the authors' own work and some of it is published here for the first time. Jones and Schoonover are both highly regarded veterans of the U.S. National Institute of Standards and Technology. With this handbook, they have provided a service and resource vital to anyone involved not only in the determination of mass, but also to the entire field of precision measurement.
Table of Contents
MASS AND MASS STANDARDS
Definition of Mass
The Mass Unit
Mass Artifacts, Mass Standards
References
Historical Background
Role of Measurement in Science
Footnotes
References
RECALIBRATION OF MASS STANDARDS
Recalibration of the U.S. National Prototype Kilogram
Third Periodic Verification of National Prototypes of the Kilogram
CONTAMINATION OF MASS STANDARDS
Introduction
Platinum-Iridium Standards
Stainless Steel Mass Standards
Mass Standards
Stainless Steel and Allied Materials
Studies of Influence of Cleaning on Stability of XSH Alacrite Mass Standards
References
CLEANING OF MASS STANDARDS
Introduction
Solvent Cleaning and Steam Washing (Nettoyage-Lavage)
Summaries of National Laboratory Studies Related to Cleaning
Cleaning of Stainless Steel Mass Standards
References
FROM BALANCE OBSERVATIONS TO MASS DIFFERENCES
Introduction
Determination of Mass Difference
References
Introduction
Measurement
Mean, Arithmetic Mean, Average
Deviation
Standard Deviation, SD
Degrees of Freedom, DF
Population
Sample
Population Standard Deviation
Variance
Random Sample
Normal Distribution of Measurements
Concept of a Limiting Mean
Central Limit Theorem
Student's t
F Test
Other Pertinent Terms
Bibliography
Reference
MEASUREMENT UNCERTAINTY
Introduction
NIST Guidelines
Example of Determination of Uncertainty
References
WEIGHING DESIGNS
Introduction
Least Squares
Sequences
Observation Multipliers for Determining Mass Values and Deviations
Factors for Computing Weight Standard Deviation Needed for Uncertainty Calculations
Calculations of Various Values Associated with Design 16 and the 5-kg, 2-kg, 2-kg2, and 1-kg Weights
Calculations of Various Values Associated with the A.1.2 Design Solution for the 1-kg and ?1-kg Weights
Commentary
References
CALIBRATION OF THE SCREEN AND THE BUILT-IN WEIGHTS OF A DIRECT-READING ANALYTICAL BALANCE
Calibration of the Screen
Calibration of the Built-In Weights
References
A LOOK AT THE ELECTRONIC BALANCE
Introduction
The Analytical Balance and the Mass Unit
Balance Principles
A Closer Look at Electronic Balances
Benefits and Idiosyncrasies of Electronic Balances
Black Box Comparison
The Future
References
BUOYANCY CORRECTIONS IN WEIGHING
Introduction
Buoyant Force and Buoyancy Correction
Application of the Simple Buoyancy Correction Factor to Weighing on a Single-Pan Analytical Balance
The Electronic Analytical Balance
Usual Case for Which the Air Density Is Not the Reference Value
Examples of Effects of Failure to Make Buoyancy Corrections
Other Examples of Buoyancy Correction
References
AIR DENSITY EQUATION
Introduction
Development of the Jones Air Density Equation
Weight of Dry Air
CIPM-81 Air Density Equation
CIPM 1981/1991 Equation
Recommendation
Direct Determination of Air Density
Experimental Determination of Air Density in Weighing on a 1- Kilogram Balance in Air and in Vacuum
A Practical Approach to Air Density Determination
Test of Air Density Equation at Differing Altitude
References
DENSITY OF SOLID OBJECTS
Development of a Density Scale Based on the Density of a Solid Object
Principles of Use of the Submersible Balance
Determination of Density of Mass Standards; Requirement and Method
The Density of a Solid Object by Hydrostatic Weighing
An Efficient Method for Measuring the Density (or Volume) of Similar Objects
References
CALCULATION OF THE DENSITY OF WATER
Introduction
Formulations of Wagenbreth and Blanke
Kell's Formulations
Conversion of IPTS-68 to ITS-90
Redeterminations of Water Density
Change in Density of Water with Air Saturation
Density of Air-Saturated Water on ITS-90
Compressibility-Corrected Water Density Equation
Effect of Isotopic Concentrations
Estimation of Uncertainty in Water Density Due to Variation in Isotopic Concentrations
Summary
References
CONVENTIONAL MASS; CONCEPT, INTENT, BENEFITS, AND LIMITATIONS
Introduction
Conventional Value of Weighing in Air
Examples of Computation
Discussion
Example 1
Example 2
Example 3
Example 4
Conclusions
References
A COMPARISON OF ERROR PROPAGATIONS FOR MASS AND CONVENTIONAL MASS
Introduction
Steel Standard of Mass S and Density 7.950 g/cm3
g/cm3 with a Stainless Steel Standard of Mass S
Maximum Permissible Errors on Verification
Uncertainty Trade-Offs
Summary
References
EXAMINATION OF PARAMETERS THAT CAN CAUSE ERROR IN MASS DETERMINATIONS
Introduction
Mass Comparison
The Fundamental Mass Comparison Relationship
Uncertainties in the Determination of X Due to Uncertainties in the Parameters in Equation (17.2)
Buoyancy
Thermal Equilibium
Atmospheric Effects
Magnetic Effects
Instability of IPK
Cleaning
Conclusions
Discussion
References
DETERMINATION OF THE MASS OF A PISTON-GAGE WEIGHT, PRACTICAL UNCERTAINTY LIMITS
Introduction
Assignment of Mass
References
RESPONSE OF APPARENT MASS TO THERMAL GRADIENTS AND FREE CONVECTIVE CURRENTS
Thermal Gradients
Free Convective Currents
References
MAGNETIC ERRORS IN MASS METROLOGY
Introduction
Magnetic Force
References
EFFECT OF GRAVITATIONAL CONFIGURATION OF WEIGHTS ON PRECISION OF MASS MEASUREMENTS
Introduction
Magnitude of the Gravitational Configuration Effect
Significance of the Gravitational Configuration Correction
References
BETWEEN-TIME COMPONENT OF ERROR IN MASS MEASUREMENTS
Introduction
References
LABORATORY STANDARD OPERATING PROCEDURES
Introduction
Environmental Controls
Balances
Mass Standards
Weight Cleaning
Weighing
Statistical Surveillance
Routine Bookkeeping
Reference
CONTROL CHARTS
Introduction
Procedure
Types of Control Charts
Updating Control Charts
Interpretation of Control Chart Tests
Reference
TOLERANCE TESTING OF MASS STANDARDS
Introduction
Prerequisites
Methodology
Procedure--Option A, Use of Single-Pan Balance
Procedure--Option B, Use of Full Electronic Balance
Procedure--Option C, Use of Equal Arm Balance
Tolerance Evaluation
Reference
SURVEILLANCE TESTING
Introduction
Types of Surveillance Tests
Surveillance Limits
Surveillance Charts
Identification of Weights the Mass of Which Has Changed
References
THE MASS UNIT DISSEMINATED TO SURROGATE LABORATORIES USING THE NIST PORTABLE MASS CALIBRATION PACKAGE
Introduction
Review
The Third Package
Hardware and Software
The Measurements
Data
Analysis
Conclusions
References
HIGHLY ACCURATE DIRECT MASS MEASUREMENTS WITHOUT THE USE OF EXTERNAL STANDARDS
Introduction
The Force Detector
Discussion of the Method
Uncertainties
Balance Selection
Balance
Discussion
Direction of Future Developments in Electronic Balances and Their Uses
References
THE PIGGYBACK BALANCE EXPERIMENT; AN ILLUSTRATION OF ARCHIMEDES' PRINCIPLE AND NEWTON'S THIRD LAW
Introduction
The Piggyback Thought Balance Experiment
The Laboratory Experiment
Conclusion
References
THE APPLICATION OF THE ELECTRONIC BALANCE IN HIGH PRECISION PYCNOMETRY
Introduction
Pycnometer Calibration
Apparatus
Analysis
Data
Discussion
References
APPENDICES
Buoyancy Corrections in Weighing Course
Examination for Buoyancy Corrections in Weighing Course
Answers for Examination for Buoyancy Corrections in Weighing Course
Maximum Permissible Errors (MPE)
Minimum and Maximum Limits for Density of Weights
Density and Coefficient of Linear Expansion for Pure Metals, Commercial Metals, and Alloys
Linearity Test
Editorial Reviews
"This book will clearly become the definitive reference source for all those concerned with measurement of mass, whether in basic science, engineering, or commerce. It encapsulates a unique range of practical experience that has not been recorded before."
-David R. Lide, Former Director, Standard Reference data, NIST and Editor-in-Chief of the CRC Handbook of Chemistry and Physics
From David Lide, Former Director, NIST and Editor-in-Chief of the CRC Handbook of Chemistry and Physics:
"Weights and measures may be ranked among the necessaries of life … They are necessary to every occupation of human industry; to the distribution and security of every species of property … The kn
owledge of them, as in established use, is among the first elements of education, and is often learned by those who learn nothing else, not even to read and write. This knowledge is riveted in the memory by the habitual application of it to employments of men throughout life."
-John Quincy Adams, 1821
